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The hydrogen atom is investigated, within a pseudo-complex extension of thecoordinates and momenta, which introduces a minimal length scale (l) andresults into a non-commutative Quantum Mechanics. After resuming thepseudo-complex extension of Quantum Mechanics, the modified energies of thehydrogen atom are deduced, producing corrections of the order of the square ofthe minimal length scale. Using the Lamb Shift, we obtain an upper boundary forthe minimal length scale l, orders of magnitude more restrictive than formerestimations.

The Hydrogen Atom within a pseudo-complex Quantum Mechanics, involving a minimal length